4 Answers
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Shows and movies may do this for several reasons: to keep audiences around for longer, production breaks, financial reasons, actors signed on for other projects that interfere with shooting of a season, to ramp up other projects that needed more time, just to name a few.

In the case of Breaking Bad, Brian Cranston indicated that they planned to shoot the first 8 episodes, then take a 4 month break from production with the intent of filming those then having the series air sometime in 2013.

Then you have movies that do it, like the Harry Potter franchise. The reasoning given there was that the final book was so dense with material that trying to fit it all in a single movie, even a super long one, wouldn't do it justice.

Production teams and writers decide to break up a season or a movie for several reasons:

The Material is simply too much for one season or movie, but cannot be converted to another episode/season.

The initial cost estimate was for a limited season only, but later they changed it to have more episodes or parts.

Sometimes, when the list of episodes is large enough, the company might break it up into two parts for marketing, distribution and broadcast purposes.

The shooting schedule forces them to shoot the season in two or more parts.

A break in production for any reason could force the producers to release the first half while the second half is still being/will be created.

The producers and directors want to focus on more detail and visuals, i.e. on quality, and hence take time to craft the episodes over a period of time.

As for the TV series you mentioned:

Sex and the City Season 6: The sixth season aired in two parts: from June until September 2003 and during January and February 2004 due to production schedules. (No official sources to cite)

Entourage Season 3: Similarly, the third season aired in two parts: the show was produced and shot in different timelines of the year. Also, the season was expanded from its initial run.

The Sopranos Season 6: Possibly due to it being the finale, and the large number of material and episodes to create.

Breaking Bad Season 5: It was split up into two parts because of Production and length, material, quality of the plot. Also please read the news article-

In early August 2011, negotiations began over a deal regarding the fifth and possibly final season between AMC and Sony Pictures Television, the production company of the series. AMC proposed a shortened fifth season (six to eight episodes, instead of thirteen) to cut costs, but the producers declined. Sony then approached other cable networks about possibly picking up the show if a deal could not be made.[33] On August 14, 2011, a deal was made in which AMC renewed the series for a final 16-episode season.

Note: Even though the title says Season X - Part I or II, the media, critics and award committees consider each Part to be a separate season on their own. They get separate ratings, separate awards and separate accolades.

In at least some of these cases, a single season was filmed during the show's usual shooting schedule, shown the same year, and then released on DVD in two parts. This is typically a marketing decision - you'll note that the cost of the two parts of a season is invariably greater than the cost of a single season.